Adaptive Experimentation Can Hide Model Error:Detection Limits and Falsification Budget

Scientific discovery systems typically optimize experiments within a fixed hypothesis space. This creates a failure mode when all available candidates omit the same missing mechanism: candidate disagreement can collapse even while the model class is systematically wrong. We formulate experimental model-class revision, in which a discovery policy jointly proposes a structural edit and a diagnostic experiment that tests whether that edit is necessary. The method couples a class-level distinguishability objective, in which one shared parameterization must explain all selected experiments, with anytime-valid sequential evidence that triggers structural revision only after the current class is rejected. On 400 held-out controlled dynamical environments, the joint policy reaches 89.5% exact recovery with a budget of 32 real experiments, improving the strongest matched baseline by 10.0 percentage points while requiring fewer executed experiments and candidate fits. The learned revision-experiment pairing transfers across unseen mechanism combinations, held-out but expressible primitives, parameter extrapolation, and shifted experiment costs; when the true mechanism is outside the edit grammar, it detects library insufficiency in 88% of cases with a 5.5% false-support rate. Revision gains also transfer to ODEBench and ODEBase model-library tasks, as well as DiscoverPhysics worlds. These results support a view of scientific discovery in which deciding what mechanisms a theory should make expressible and where to collect evidence are treated as a single sequential decision problem.

The advantages of adaptive experiments have led to their rapid adoption in economics, other fields, and among practitioners. However, adaptive experiments pose challenges for causal inference. This note suggests a BOLS (batched ordinary least squares) test statistic for inference on treatment effects in adaptive experiments. The statistic provides a precision-equalizing aggregation of per-period treatment-control differences under heteroskedasticity. The combined test statistic is a linear combination of heteroskedastic per-period z-statistics and can be used to construct asymptotically valid confidence intervals. We provide simulation results comparing rejection rates in the typical case with few treatment periods and few (or many) observations per batch.

Randomized Controlled Trials (RCTs) represent the gold standard for causal inference yet remain a scarce resource. While large-scale observational data is often available, it is utilized only for retrospective fusion, and remains discarded in prospective trial design due to bias concerns. We argue this "tabula rasa" data acquisition strategy is fundamentally inefficient. In this work, we propose Active Residual Learning, a new paradigm that leverages the observational model as a foundational prior. This approach shifts the experimental focus from learning target causal quantities from scratch to efficiently estimating the residuals required to correct observational bias. To operationalize this, we introduce the R-Design framework. Theoretically, we establish two key advantages: (1) a structural efficiency gap, proving that estimating smooth residual contrasts admits strictly faster convergence rates than reconstructing full outcomes; and (2) information efficiency, where we quantify the redundancy in standard parameter-based acquisition (e.g., BALD), demonstrating that such baselines waste budget on task-irrelevant nuisance uncertainty. We propose R-EPIG (Residual Expected Predictive Information Gain), a unified criterion that directly targets the causal estimand, minimizing residual uncertainty for estimation or clarifying decision boundaries for policy. Experiments on synthetic and semi-synthetic benchmarks demonstrate that R-Design significantly outperforms baselines, confirming that repairing a biased model is far more efficient than learning one from scratch.